### Question 30 exam 2020

Hello,

I don't see how to obtain the expression for the excess cost function $$f(x) - f(x^*)$$. My problem is that I have an additional term than in the solution, namely $$x^*H(x - x^*)$$ obtained by replacing $$q = H x^*$$.

Top comment

Hi,
I think you forgot to substract the value of $$f(x^*)$$.
Replacing $$q = H x^*$$ you get that $$f(x) = \frac{1}{2} x^\top H x - x^T H x^*$$ and $$f(x^*) = - \frac{1}{2} {x^*}^\top H x^*$$,
hence $$f(x) - f(x^*) = \frac{1}{2} (x - x^*)^\top H (x - x^*)$$.
Hope this helps.
Scott

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